A stable finite element method for low inertia undulatory locomotion in three dimensions
| Autor: | Ranner, T |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
Applied Mathematics media_common.quotation_subject Numerical analysis Mathematical analysis Numerical Analysis (math.NA) 010103 numerical & computational mathematics Orthonormal frame Inertia 01 natural sciences Finite element method 010101 applied mathematics Piecewise linear function Computational Mathematics Undulatory locomotion FOS: Mathematics Piecewise Mathematics - Numerical Analysis 0101 mathematics Orthonormality media_common Mathematics |
| Zdroj: | Applied Numerical Mathematics. 156:422-445 |
| ISSN: | 0168-9274 |
| Popis: | We present and analyse a numerical method for understanding the low-inertia dynamics of an open, inextensible viscoelastic rod - a long and thin three dimensional object - representing the body of a long, thin microswimmer. Our model allows for both elastic and viscous, bending and twisting deformations and describes the evolution of the midline curve of the rod as well as an orthonormal frame which fully determines the rod's three dimensional geometry. The numerical method is based on using a combination of piecewise linear and piecewise constant finite element functions based on a novel rewriting of the model equations. We derive a stability estimate for the semi-discrete scheme and show that at the fully discrete level that we have good control over the length element and preserve the frame orthonormality conditions up to machine precision. Numerical experiments demonstrate both the good properties of the method as well as the applicability of the method for simulating undulatory locomotion in the low-inertia regime. |
| Databáze: | OpenAIRE |
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